Preparation

Season the chicken with salt and pepper to taste. In a large high-sided skillet with a lid, heat 1 tablespoon of oil over medium-high heat. Cook the chicken until it begins to brown and releases easily from the pan, about 5 minutes. Flip the chicken and cook until the other side is browned, an additional 4 to 5 minutes. Transfer the browned chicken to a plate and set it aside.
Reduce the heat to medium and add another tablespoon of oil. Add the onion to the pan and cook until it has softened, about 2 to 3 minutes. Add the garlic and cook, stirring, for an additional 30 seconds. Add the flour and cook, stirring, for about 1 minute. While whisking, slowly add the broth. Continue to whisk until the liquid begins to thicken, 1 to 2 minutes. Add the asiago cheese and continue to whisk until it is fully incorporated. Stir in the rosemary.
Return the chicken to the pan, flip it in the sauce to coat and then cover it. Continue to cook until the chicken reaches an internal temperature of 165ºF, about 6 minutes.
Serve immediately or store in the refrigerator for up to 3 days.